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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>The effort that is expended in evaluation of the definite integrals that define the coefficients the <span class="process-math">\(a_0\text{,}\)</span> <span class="process-math">\(a_n\text{,}\)</span> and <span class="process-math">\(b_n\)</span> in the expansion of a function <span class="process-math">\(f\)</span> in a Fourier series is reduced significantly when <span class="process-math">\(f\)</span> is either an even or an odd function. Recall that a function <span class="process-math">\(f\)</span> is said to be</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\text{{\bf even}~ if } f(-􏰠x)=f(x)\quad \text{ and }\quad \text{{\bf odd}~ if } f(-􏰠x)=-􏰠f(x).
\end{equation*}
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<p class="continuation">The following theorem lists some properties of even and odd functions.</p>
<span class="incontext"><a href="sec7_5.html#p-364" class="internal">in-context</a></span>
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